Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic36 | C2 | semidirect |
| 4. C2×#63376 | C2 | semidirect |
| 5. #10588229 | C2 | semidirect |
| 67. C23×C9 | Q16 | semidirect |
| 221. C9 | #2001 | semidirect |
| 226. C23 | Dic36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63486 | 2 |
| C22×Dic36 | 2 |
| C2×C9×C22⋊C8 | 2 |
| C2×#63376 | 2 |
| #10588229 | 2 |
| #69964 | 3 |